What "generally accepted truths" does Atticus challenge in his final appeal in To Kill a Mockingbird?
Most obviously during his speech, Atticus makes a point to challenge the generally accepted beliefs of the majority of white people, including the jurors, during the 1930s that all blacks are inferior, ill-behaved, and of low morals. He argues that just as there are black people of low morals, there are people of all races with low morals.
Atticus also challenges the well-known quote of Thomas Jefferson that -
"All men are created equal."
Atticus contends that although this phrase has become a part of the American culture and is often repeated, it is not true if taken out of context. He argues that in many instances, people are not created equally by God and that some are smarter than others or better at one thing or another than others. Atticus argues that in reality, all people are unequal in many ways and should be treated differently in settings such as schools. However, he states that with regard to the courts, the one place where all people should be created and treated equally, many times people are not. He challenges the jury to set aside the generally accepted prejudices against black men and to truly believe that in the court, all men are created equally.
I believe that you are talking about Atticus's speech in Chapter 20. In that speech, he challenges a few generally accepted truths. The first of these truths is that black people lie all the time. The second is that any incident between a white woman and a black man is the fault of the black man. (This second assumption was behind many of the lynchings of black people that actually happened in the South in our history.)
Atticus says that the testimony against Robinson was based on the idea that no one would believe Tom because everyone knows that "Negroes" lie. He also says it is based on the idea that black men are constantly lusting after white women and cannot be trusted around them. Atticus argues that neither of these is true in this case.